Culture and cognitive development: studies in mathematical understanding PDF
Preview Culture and cognitive development: studies in mathematical understanding
CULTURE AND COGNITIVE DEVELOPMENT: Studies in Mathematical Understanding This page intentionally left blank CULTURE and COGNITIVE DEVELOPMENT: Studies in Mathematical Understanding GEOFFREY B. SAXE University of California, Los Angeles \T I Psychology Press M Taylor &. Francis Group New York London Copyright © 1991 by Lawrence Erlbaum Associates, Inc. All rights reserved. No part of this book may be reproduced in any form, by photostat, microform, retrieval system, or any other means, without the prior written permission of the publisher. First published 1991 by Lawrence Erlbaum Associates, Inc., Publishers 365 Broadway Hillsdale, New Jersey 07642 This edition published 2014 by Psychology Press Psychology Press Psychology Press Taylor & Francis Group Taylor & Francis Group 711 Third Avenue 27 Church Road New York, NY 10017 Hove, East Sussex BN3 2FA Psychology Press is an imprint of the Taylor & Francis Group, an informa business Library of Congress Cataloging-in-Publication Data Saxe, Geoffrey B. Culture and cognitive development : studies in mathematical understanding / Geoffrey B. Saxe, p. cm. Includes bibliographical references and indexes. ISBN 0-8058-0273-8 1. Mathematics—Study and teaching. 2. Cognition and culture. I. Title. QA11.S142 1990 370.15'651—dc20 90-40923 CIP Contents Preface vii PART I. CULTURE AND COGNITION: A METHOD OF STUDY 1 1. Culture and Cognitive Development 3 2. A Research Approach 15 PART II. COMPONENT 1: EMERGENT MATHEMATICAL GOALS 29 3. Parameter 1: The Structure of the Candy-selling Practice 32 4. Parameters 2 and 3: Social Interactions and Practice-linked Artifacts and Conventions—A Focus on the Sell Phase 36 5. Parameters 2 and 3: Social Interactions and Practice-linked Artifacts and Conventions—A Focus on the Purchase Phase 47 6. Parameter 4: Sellers’ Emergent Mathematical Goals and Their Prior Understandings 57 7. Emergent Mathematical Goals of the Practice: A Summary and Discussion of the First Analytic Component Applied to the Candy-selling Practice 63 v Vi CONTENTS PART III. COMPONENT 2: FORM-FUNCTION SHIFTS IN CANDY SELLERS’ MATHEMATICS 67 8. The Influence of Practice Participation on Sellers’ Mathematics 69 9. The Development of Sellers’ Mathematics 101 10. Form-function Shift in Sellers’ Mathematics: Links between Components 1 and 2 132 PART IV. COMPONENT 3: THE INTERPLAY BETWEEN LEARNING IN AND OUT OF SCHOOL 135 11. Some Contrasts between Mathematics of the School and of the Candy-selling Practice 142 12. The Influence of Schooling on Sellers’ Mathematics 152 13. The Influence of Selling Experience on Learning Mathematics in School 162 14. Appropriation and Specialization in the Practice 174 PART V. CULTURE AND COGNITIVE DEVELOPMENT 181 15. Epilogue 183 Appendix A: Recruitment of Sellers 187 Appendix B: Background Information on Sellers and Their Practice 188 Appendix C: Extended Description of Tasks 191 References 198 Author Index 205 Subject Index 208 Preface This volume has taken form through the help and support I received from various teachers, colleagues, friends, and family. I am grateful to them all. As a graduate student, I studied with Jonas Langer; his rich insights into problems of cognitive development continue to be important to me in working through the conceptual problems that I have struggled with in this volume and in my previous work. I also owe much to other individuals during my undergradu ate and graduate work in these earlier years. Elliot Turiel was influential in introducing me to structural-developmental approaches to cognition, and under his supervision while I was an undergraduate, I was introduced to problems of extending structural-developmental approaches to field settings in a project on social cognition in Lower Kalskag, Alaska. His more recent work on domain distinctions in developmental analyses of social cognition has continued to influ ence my own thinking. Allen Black, and a community of graduate students working with Jonas at Berkeley provided a wonderful intellectual environment to pursue questions of cognitive development, and much of my own ways of con ceptualizing problems of cognitive development has its roots in weekly meetings with Jonas and these friends. I have also benefited by contact with various colleagues in my postdoctoral years. As a postdoctoral fellow under a National Institute of Mental Health training grant, I was introduced to problems of comparative research through the study of atypical cognitive development and the breakdown of cognitive func tioning following brain injury at The Children’s Hospital Medical Center in Boston under the guidance of Peter Wollf and at the Boston Veteran’s Admin istration Hospital under the guidance of Howard Gardner. In the Papua New Guinea work that I summarize in the volume, I am indebted to the help and vii viii PREFACE support of David Lancy, Randall Souviney, Tom Moylan, Virginia Guilford, Marshall Lawerence, and numerous other unnamed individuals. During my years on the faculty at the Graduate Center of the City University of New York, short but fruitful discussions with Michael Cole and Joseph Glick were important to me. In accomplishing the body of the work on child candy sellers described in this volume, I benefited greatly from the supportive research environment created by Analucia Schliemann, Terezinha Carraher, and David Carraher at the Univer- sidade de Pernambuco in Recife. Luciano Meira, a student at the Universidade de Pernambuco, assisted in many phases of the conduct of this project. Though a masters student at the time, Luciano functioned in many ways as an extraor dinarily able colleague. In addition, Wilher dos Santos, Anna Ruiz, Danielle, and Marcia were students that assisted in field work and interviews throughout the project, and the high quality of data on which this volume is based collected is due to their fine efforts. Scott Lewis, a graduate student at UCLA, was very helpful in administering the interviews to the U.S. schooled sample described in Part IV. Maryl Gearhart, Steven Guberman, Joe Becker and Marta Laupa each read and commented on some parts of or various drafts of this manuscript. In address ing their criticisms, I have been led to new insights, and I was able to make this manuscript more readable and coherent. I am deeply grateful for the patience and support of my family—Maryl, Josh, and Ben (who was bom a Brazilian)—on which this volume has taken a toll. Maryl, in particular, has played many roles in my research activities since my early work in Papua New Guinea—wife, friend, close colleague, teacher, and constructive critic. She deserves special thanks for much that is good about this work and my prior work. Finally, the support that my parents and sister have provided over the years has been instrumental to me in forming and accomplishing goals that have led to this volume. From my first trip around the U.S. as a young teenager to a stay in a remote part of Alaska as an undergraduate to my more recent efforts in non- Westem and more Western settings, I have felt warmly supported and encouraged by each of them. ACKNOWLEDGMENTS The research described in this volume would not have been possible without funding, and I am very grateful to several agencies that provided support. During my stay in Recife, I was supported by a Fulbright/CAPES fellowship, and the research itself and subsequent analyses were funded by a grant from the National Science Foundation (#BNS-85-09101). In addition, direct support of the re search was provided by a small grant administered by UCLA through the PREFACE IX Spencer Foundation, and the last phases in the writing and preparation of this manuscript were conducted while I was supported by grants from the Spencer Foundation (#M890224) and the National Science Foundation (#MDR- 8855643). The opinions expressed in this volume are my own and not necessarily those of the funding agencies.
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